Question

if alpha, bita, gama,are the roots of f(x) =
axbx' + cx + d. then 1/a + 1/B
+ 1/4 =

O b/d
O c/d
O -c/d
O -c/a​

Answer 1

Step-by-step explanation:

Correct Question :-

• If α, β and γ are the roots/zeroes of polynomial f(x) = ax³ + bx² + cx + d. Then, 1/α + 1/β + 1/γ = ?

Solution :-

Given -

• If α, β and γ are zeroes of polynomial f(x) = ax³ + bx² + cx + d

To Find -

Value of 1/α + 1/β + 1/γ

→ βγ + αγ + βα/αβγ

→ αβ + βγ + γα/αβγ

Now,

As we know that :-

• αβγ = -d/a

And

αβ + βγ + γα = c/a

Then,

The value of 1/α + 1/β + 1/γ or αβ + βγ + γα/αβγ is

→ c/a ÷ -d/a

→ c/a × -a/d

→ -c/d

Hence,

The value of 1/α + 1/β + 1/γ is -c/d.

Hence,

Option (3) is correct.

Additional information :-

For a quadratic polynomial :-

• α + β = -b/a
• αβ = c/a

And

For a cubic polynomial :-

• α + β + γ = -b/a
• αβγ = -d/a
• αβ + βγ + γα = c/a

Answer 2

$\large{\boxed{\underline{\underline{\bf{\red{Answer:-}}}}}}$

$\large\underline\mathrm{The \: value \: of \: 1 \: / \: alpha \: + \: 1 \: / \: beta \: + \: 1 \: / \: Gamma \: is \: - \: c \: / \: d \: .}$

$\large\underline\mathrm{and \: correct \: options \: is \: (3)}$

$\large\underline\mathrm{Given:-}$

• If alpha beta and gamma are zeros of polynomial f(x) = ax³ + bx² + CX + d.

$\large\underline\mathrm{To \: find}$

• Volue of 1/alpha + 1/beta + 1/Gamma

$\implies$ (beta gamma) + (alpha Gamma) + *beta alpha)/(alpha beta gamma)

$\implies$ (alpha beta + beta gamma + Gamma alpha) / (alpha beta gamma)

$\large\underline\mathrm{Now}$

$\implies$ (alpha beta gamma) = -d/a

$\large\underline\mathrm{And}$

$\implies$ (alpha beta + beta gamma + Gamma alpha) = c/a

$\large\underline\mathrm{Then,}$

The value of 1/alpha + 1/beta + 1/Gamma or (alpha beta + beta gamma + Gamma alpha) / (alpha beta gamma) is.

$\implies$ c/a = -d/a

$\implies$ c/a × -a/d

$\implies$ -c/d

$\large\underline\mathrm{hence,}$

$\large\underline\mathrm{The \: value \: of \: 1 \: / \: alpha \: + \: 1 \: / \: beta \: + \: 1 \: / \: Gamma \: is \: - \: c \: / \: d \: .}$

$\large\underline\mathrm{and \: correct \: options \: is \: (3)}$

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$